Level 5 to 40

There are two low level acrobatics trainers. One in the Imperial City and the other in the city of Anvil. If you're in the Fighter's Guild, it's worth noting that you can get some free training out of Quill-Weave in the Rats quest.

Ida Vlinorman: She's an Imperial in the Elven Gardens District of the Imperial City. If she's not in her house, look for her on the road to Chorrol or in the Arena where she gambles.

Quill-Weave: She's an Argonian in the main Anvil section. If she's not at home, check The Count's Arms or Lelles' Quality Merchandise. Bonus: If you're in the Fighter's Guide, you can get free training from her. SPOILER ALERT: During the Rats quest, your very first in the guild, talk to her after catching her red-handed, if you let her off the hook, talk to her again later to get free training.

Level 40 to 70

There are two advanced acrobatics trainers. One in Cheydinhal and one in Leyawiin.

Ganredhel: She's a Bosmer in the city of Cheydinhal. She'll train anyone, but she's associated with the Thieves Guild, so if you're a member she'll have a higher disposition. She's in her house in the morning, leaves early for Borba's Goods and Stores, then goes back home before leaving for Newlands Lodge. She'll be in the chapel in the evenings, she'll be in sneak mode.

Tsrava: She's a Khajit in the city of Leyawiin. She lives in J'bari's house, J'bari is a master trainer in light armor by the way. They're both available all day in the house.

Level 70 to 100

Torbern is the Nord master trainer of acrobatics. To find him, talk to either Ganredhel or Tsrava after reaching level 70 in acrobatics. Either of them will point you to Aerin in Aerin's Camp. Aerin's camp is North and slightly east of Cheydinhal, East of Bruma and East of Azura's Shrine if you've found it. The closest map marker is Kingscrest Cavern, slightly South-West of Aerin's Camp. Once you get there, Torbern will tell you that Aerin isn't there, but he'll offer to train you instead.